Discrete Transforms for Image Processing
We know from time-domain signal analysis that Fourier series gives an alternative representation of a periodic signal in terms of sinusoids whose frequencies are integer multiples of the fundamental frequency of the signal and whose amplitude and phase can be determined from the signal itself. These sinusoids are so-called basis functions and form a complete orthogonal set for the signal expansion. Thus one can use these sinusoids in representing the signal at each instant of time. Similarly, we use the Fourier transform for the representation of aperiodic time-domain signals. Digital images, which are 2-D discrete-space signals, can be described alternatively by discrete orthogonal ...